2011 | OriginalPaper | Buchkapitel
R-sectoriality of Cylindrical Boundary Value Problems
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We prove
$$ \mathcal{R} $$
-sectoriality or, equivalently,
L
p
-maximal regularity for a class of operators on cylindrical domains of the form
$$ \mathbb{R}^{n-k}\times V $$
, where
$$ V \subset \mathbb{R}^{k} $$
is a domain with compact boundary,
$$ \mathbb{R}^{k} $$
, or a half-space. Instead of extensive localization procedures, we present an elegant approach via operatorvalued multiplier theory which takes advantage of the cylindrical shape of both, the domain and the operator.